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Journal of the Optical Society of America B

Efficient hyperentanglement purification using a Λ system coupled with a whispering-gallery-mode microresonator

Dezhi Chen, Chang Shi, Tie-Jun Wang

Published Jan 30, 2018• 1 citation
Publisher

Abstract

Entanglement purification is of great importance in long-distance quantum communications and distributed quantum computations. Here we present an efficient scheme for the hyperentanglement purification (HP) of a two-photon system by using a high-dimensional logical gate device which is composed of atoms and a quantized whispering-gallery-mode microresonator. In the present scheme, one can complete the HP and entanglement storage in one step without resorting to additional qubits. Compared with the conventional HP schemes in which the two-qubit two-dimensional parity-checking measurements are used to correct the bit-flip errors, our scheme, which explored the high-dimensional controlled-flip operation, shows a wide distillation range with a higher fidelity. The remaining resources of the failed HP processing can be used to purify the other pair hyperentangled photons. Therefore, the efficiency of our scheme is higher than the previous schemes. The implementation of our HP is assisted by nitrogen-vacancy centers in optical microresonators, which could be achieved with current techniques.

DOI
10.1364/josab.35.000423

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Entanglement purification is of great importance in long-distance quantum communications and distributed quantum computations. Here we present an efficient scheme for the hyperentanglement purification (HP) of a two-photon system by using a high-dimensional logical gate device which is composed of atoms and a quantized whispering-gallery-mode microresonator. In the present scheme, one can complete the HP and entanglement storage in one step without resorting to additional qubits. Compared with the conventional HP schemes in which the two-qubit two-dimensional parity-checking measurements are used to correct the bit-flip errors, our scheme, which explored the high-dimensional controlled-flip operation, shows a wide distillation range with a higher fidelity. The remaining resources of the failed HP processing can be used to purify the other pair hyperentangled photons. Therefore, the efficiency of our scheme is higher than the previous schemes. The implementation of our HP is assisted by nitrogen-vacancy centers in optical microresonators, which could be achieved with current techniques.
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Recently, two-photon six-qubit hyperentanged states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present the first scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first longitudinal momentum, and the second longitudinal momentum DOFs. Our hyper-EPP is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and SWAP gates, respectively. With these two steps, the bit-flip errors in the three DOFs can be corrected efficiently. Using SWAP gates is a universal method for hyper-EPP in the polarization DOF and multiple longitudinal momentum DOFs. The implementation of our hyper-EPP is assisted by nitrogen-vacancy centers in optical microcavities, which could be achieved with current techniques. It is useful for long-distance high-capacity quantum communication with two-photon six-qubit hyperentanglement.
Hyperentanglement has attracted much attention due to its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatial-polarization mixed hyperentangled Bell state with the errors in both the spatial-mode and polarization DOFs, resorting to the nonlinear optics of a nitrogen-vacancy (NV) center in a diamond embedded in a photonic crystal cavity coupled to a waveguide. We present the first hyperentanglement purification protocol for purifying a pair of two-photon systems in a mixed hyperentangled Bell state with the errors in two DOFs. We also propose an efficient hyperentanglement concentration protocol for a partially hyperentangled Bell pure state, which has the maximal success probability in principle. These two protocols are useful in long-distance quantum communication with hyperentanglement.
High-dimensional quantum system provides a higher capacity of quantum channel, which exhibits potential applications in quantum information processing. However, high-dimensional universal quantum logic gates is difficult to achieve directly with only high-dimensional interaction between two quantum systems and requires a large number of two-dimensional gates to build even a small high-dimensional quantum circuits. In this paper, we propose a scheme to implement a general controlled-flip (CF) gate where the high-dimensional single photon serve as the target qudit and stationary qubits work as the control logic qudit, by employing a three-level Λ-type system coupled with a whispering-gallery-mode microresonator. In our scheme, the required number of interaction times between the photon and solid state system reduce greatly compared with the traditional method which decomposes the high-dimensional Hilbert space into 2-dimensional quantum space, and it is on a shorter temporal scale for the experimental realization. Moreover, we discuss the performance and feasibility of our hybrid CF gate, concluding that it can be easily extended to a 2n-dimensional case and it is feasible with current technology.
Recently, long distance of quantum communication relies on efficient quantum repeaters, and the distribution of maximal entanglement is a key technique for it. Especially, the distribution of entanglement with high-fidelity relies on the entanglement purification and concentration. Here we present a system to realize the entanglement purification for λ-type three-level entangled quantum dots by using the whispering-gallery-mode microcavity. Also we design a parity check gate on solid qubits that allows the quantum nondemolition measurement on the remote qubits. Moreover, one can distill a high-fidelity entangled solid state ensemble from a mixed-entangled state ensemble nonlocally.
As the interaction between the photons and the environment which will make the entangled photon pairs in less entangled states or even in mixed states, the security and the efficiency of quantum communication will decrease. We present an efficient hyperentanglement purification protocol that distills nonlocal high-fidelity hyper-entangled Bell states in both polarization and spatial-mode degrees of freedom from ensembles of two-photon system in mixed states using linear optics. Here, we consider the influence of the photon loss in the channel which generally is ignored in the conventional entanglement purification and hyperentanglement purification (HEP) schemes. Compared with previous HEP schemes, our HEP scheme decreases the requirement for nonlocal resources by employing high-dimensional mode-check measurement, and leads to a higher fidelity, especially in the range where the conventional HEP schemes become invalid but our scheme still can work.